Mixing in fluid flow

Mixing by fluid flow is important in a variety of situations
in nature and technology. One effect fluid motion can have is to
strongly enhance diffusion. The extent of diffusion enhancement depends
on the properties of the flow. I will give an overview of the area, and
will discuss a sharp criterion describing a class of incompressible
flows that are especially effective mixers. The criterion uses spectral
properties of the dynamical system associated with the flow, and is
derived from a general result on decay rates for dissipative semigroups
of certain structure. The proofs rely on methods developed in studies of
wavepacket spreading in mathematical quantum mechanics.